Vol. 66, No. 1, 1976

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Weierstrass points of products of Riemann surfaces

Robert F. Lax

Vol. 66 (1976), No. 1, 191–194

Ogawa has defined sets of Weierstrass points of a holomorphic vector bundle on a compact complex manifold. We generate nontrivial examples of such sets of Weierstrass points by considering the canonical bundle on a product of Riemann surfaces.

In the first section, we review Ogawa’s definition and some classical facts about Weierstrass points on Riemann surfaces. In §2, we prove our theorems and consider an example to illustrate the proofs. Finally, we remark that a connection between Weierstrass points on a Riemann surface and fixed points of a periodic automorphism does not seem to extend to higher dimensions.

We wish to thank Pierre Conner for helpful conversations and Roy Ogawa for useful communications.

Mathematical Subject Classification 2000
Primary: 32J99
Secondary: 14H20, 32L05
Received: 9 April 1976
Published: 1 September 1976
Robert F. Lax